Such a high-pressure discharge lamp has been disclosed, for example, in the European patent specification EP 0 991 107 B1. On page 4, at lines 12 to 26 of column 6 of this patent specification, a high-pressure discharge lamp with a base at one end for a motor vehicle headlight is described which has a discharge vessel surrounded by a vitreous outer bulb, the outer bulb being provided with a transparent, electrically conductive layer which extends over the entire discharge space of the lamp. This layer is connected to the circuit-internal ground reference potential of the operating device of the high-pressure discharge lamp in order to improve the electromagnetic compatibility of the lamp.